On the Group of Diffeomorphisms Preserving a Locally Conformal Symplectic Structure

The automorphism group of a locally conformal symplectic structure is studied. It is shown that this group possesses essential features of the symplectomorphism group. By using a special type of cohomology the flux and Calabi homomorphisms are introduced. The main theorem states that the kernels of these homomorphisms are simple groups (for the precise statement, see Section 7). Some of the methods used may also be interesting in the symplectic case.